Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
Abstract
We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.
Cite
@article{arxiv.cond-mat/9908003,
title = {Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects},
author = {Ganesh Sundaram and Qian Niu},
journal= {arXiv preprint arXiv:cond-mat/9908003},
year = {2009}
}
Comments
12 pages, RevTex